The Microscopic Conversion Law: M₁-Localized Fock Sources and Parameter-Free Two-Route Quantum Cycles in Six-Throat Directed Spacetime

Paper XXVI of the Six-Throat Directed Geometry program derives the microscopic conversion law that completes the number-changing interaction left open by the preceding countable-mode quantum-field construction. It shows first that a regular affine displacement of the directed mass-potential operator cannot generate the required completed linear Fock source, because the corresponding displacement becomes singular at the mixed interfaces. The inherited logarithmic mass gradient instead provides a finite conversion layer and selects the lowest antiperiodic carrier pair with opposite directed momenta. The local directed Dirac structure supplies a finite boundary spectral split. Positive-energy projection fixes the gain-channel occupation to one half, while the two-face boundary algebra maps the equal counter-directed transfer channels into the two minimal antiperiodic carriers. In the adopted numerical witness, this determines finite carrier energy, occupation, and microscopic coupling scales. The construction distinguishes the extended mixed-face region E0 from the microscopic interaction vertex M1, identified as the Great Attractor and the center of E0. The macroscopic routing operator acts across E0 without changing particle number, whereas the number-changing Fock source is localized at M1. Two independent circulation routes are retained, and the outer interface EG performs the global return without mixing them. The complete one-particle spatial cycle has holonomy -I4, whose Fock-space lift is exactly number parity. The microscopic interaction is represented by a square-summable M1-anchored smearing rather than a point field. Under the paper's explicit minimal no-new-function selection rule, the source is normalized, centered at M1, antiperiodic, and carries the expected opposite momenta on the two routes. The earlier gradient-carrier profile and the final microscopic source are kept as distinct operator structures rather than identified as the same state. Using the adopted topological input that M1 is formed from two coherent positive primordial microscopic source contributions, each carrying one unit of normalized conversion charge, the integrated microscopic action is fixed to theta_M1 = 2. The resulting one-cycle conversion sector is therefore parameter-free. The bosonic output follows a Poisson number distribution with mean four, while the one-mode fermionic realization yields complementary vacuum and one-particle probabilities determined by the same fixed action. The four sectors defined by the directed label and circulation label have identical particle-number probabilities. The directed label remains observable in phase-sensitive source quadratures, while the circulation label remains encoded in the sign of the antiperiodic momentum. The reproducibility audit verifies all 38 declared conditions, with a maximum core residual of approximately 2.32 × 10^-13. The scope of Paper XXVI is the exact spatial conversion cycle; no physical temporal transit law is claimed or required.